Computer implemented method for providing temperature data, a computer product element and a system

The instant application claims priority to European Patent Application Nos. 22200297.4, filed Oct. 7, 2022, and 22203907.5, filed Oct. 26, 2022, each of which is incorporated herein in its entirety by reference.

The present disclosure relates to a computer implemented method for determining boundary thermal resistance data and for providing temperature data of a fluid flowing through a pipe, a system for providing temperature data of a fluid flowing through a pipe, and a respective computer program product.

Determination of temperatures are important for the operation of facilities, as being one of the main control parameters for process control. Ensuring that temperature measurements of process media are accurate and repeatable is critical.

For determination of a temperature of a medium within a pipe/vessel, typically surface temperature sensors are placed at a surface of a wall of the pipe/vessel in order to measure the temperature of this surface, and respectively determine the temperature of the medium at the other side of the wall. Another traditional temperature measurement is achieved by introducing an invasive sensor, for example a thermowell, into the pipe such that a measurement is taken downstream.

Temperature is a vital parameter for the safe and efficient operation of process facilities. But merely measuring a temperature difference does not give certainty on the condition and is of little practical use, since there are many situations in reality where there are spatial inhomogeneities in the temperature field across and along the pipe/vessel. Existing state of the art invasive or non-invasive sensors will not capture these circumstances.

It has now become apparent that there is a further need to provide an improved method for providing determining boundary thermal resistance data and/or for providing temperature data of a fluid flowing through a pipe.

In view of the above, the present disclosure describes an improved method for determining boundary thermal resistance data and/or providing temperature data of a fluid flowing through a pipe. It is in particular an object of the present invention to provide a method with a more accurate boundary layer resistance calculation, in which flow data may be determined.

According to a first aspect of the present disclosure, a computer implemented method for providing temperature data of a fluid flowing through a pipe is provided, comprising: obtaining first temperature data from a first temperature sensor, which is arranged at a first pipe section; obtaining second temperature data from a second temperature sensor, which is arranged at a second pipe section; wherein the first temperature sensor and the second temperature sensor are non-invasive temperature sensors; providing process condition data; determining boundary thermal resistance data of a boundary layer of the fluid next to an inner surface of the pipe wall of the pipe based on said process condition data and/or based on the first temperature data and/or the second temperature data; optionally, determining the temperature data of the fluid based on at least the first and/or second temperature data and the boundary thermal resistance data of the boundary layer.

In one embodiment, the first and second temperature sensors are arranged spatially offset. That means that the first and second temperature sensors are distanced from each other in a longitudinal and/or a circumferential direction. The first and second pipe sections describe the positions where the first and second temperature sensors are arranged.

1 FIG. 12 12 11 12 11 11 shows a longitudinal cut of a pipe. The pipehas a diameter D and a finite wall thickness. A fluidflows through the pipe. The fluidcan be in liquid form or gaseous. Here, the fluid is gaseous. The direction of the flow of the fluidis illustrated by arrows.

1 2 FIGS.and 13 14 13 14 13 14 In the embodiment of, an embodiment with a first and second temperature sensor,is shown. The first and second temperate sensor,are both non-invasive. The two temperature sensors,are positioned circumferentially opposite to each other or alternately positioned at a measured angle from a reference point.

13 1 14 2 12 1 2 19 19 12 12 The first temperature sensoris arranged on a first pipe section Sand the second temperature sensoris arranged on a second pipe section S. Both sensors are in direct contact with the pipe. The first and second pipe sections S, Sdescribe different sections of a surface of the pipe wall. The outer surface of the pipe wallcan comprise for example a mantel of the pipeor an insulation arranged around the pipe.

13 14 13 14 13 14 2 FIG. In this embodiment, the two non-invasive sensors,are positioned in such a way, that the fluid temperature Tm dominates the measurement of one of the temperature sensors,(). Here the first temperature sensoris dominated by the fluid temperature Tm and the second temperature sensoris dominated by the condensate temperature Tcon.

13 14 In this embodiment, a nominal process temperature Tn (not shown) is used in the comparison model to determine the predicted surface temperature Tsp. The difference of the predicted temperature Tsp to the first temperature sensorand the second temperature sensormay be used to determine stratification and the temperature distribution.

12 The comparison model can be further improved for example by using the distance from the inlet and/or the radius R of curvature at a bend in the pipeprior to the measurement point. Upstream flow disturbances can reduce stratification, so that the stratification will grow with the distance from the disturbances. Measuring this growth, for example by multiple sensor setups, can give additional flow data F and hence confirmation of any low-flow-stratification effect.

15 16 12 15 16 15 11 15 11 FIG. 4 FIG. A boundary layeris located on the inner pipe wall surfaceof the pipe(see for example). The boundary layeris defined as the fluid layer close to the inner pipe wall surface. The boundary layeris relatively slow compared to the mainstream of the fluid. The boundary layerhas a thermal boundary layer resistance Rbl. The thermal boundary layer resistance Rbl is part of a resistance network (cf.).

12 The resistance network connects a fluid temperature Tm with the surface temperature Ts of the outer surface of the pipe wall of the pipe.

2 FIG. 1 FIG. 21 21 relates toand graphically illustrates the difference between the normal flow of the gas without condensation and situations when condensateoccurs and data to support possible flow regimes. If the difference between the fluid temperature Tm and the surface temperature Ts deviates from the predicted temperature, condensateaccumulation can be suspected. In the same way as condensates, of course also solidification, crystallization or other types of build-ups can be detected since they will create a modified thermal boundary layer resistance Rbl.

3 FIG. 3 FIG. 12 shows a cross section of a pipe.shows components of the resistance network connecting the fluid temperature Tm and a surface temperature Ts.

4 FIG. 3 FIG. 12 18 is a schematic view of the resistance network. The resistance network comprises the pipe thermal resistance Rp and the external resistance Ra, which depends on outside conditions. The pipemay be also covered with an insulation(cf.). Then, an additional insulation resistance Rins is added to the resistance network.

11 12 15 The fluid temperature Tm, which is the volume or mass average temperature of the fluidis estimated by relating the surface temperature Ts to the fluid temperature Tm, via the thermal resistance network. The surface temperature Ts of the pipefor a given process condition data P is dependent on thermal resistance Rbl of the boundary layer.

The process condition data P comprises physical data regarding the fluid and pipe parameters for determining the thermal boundary resistance Rbl. For example, nominal flow rate, pressure, density, viscosity, pipe dimensions, wall thickness and thermal conductivity.

13 1 Ts is provided by the first temperature sensor. Ts corresponds to the first temperature data T. Ta is an external temperature. Ta is a reference temperature and can be measured by third sensor (not shown) or can be input into the model.

The method derives a value for the boundary layer resistance Rbl process conditions P. The boundary layer resistance Rbl is by one embodiment expressed as a function of the Reynolds number Re and the Prandtl number Pr which characterize the flow/thermal condition of the fluid. Several situations can lead to variation in boundary layer resistance Rbl without knowledge of the processing software and cause a measurement error. Factors which cause variation in boundary layer resistance, are changing flowrates or flow regimes laminar, transitional, and turbulent regimes, distance of the measurement location from the pipe inlet, upstream flow distorting features like bends, and occurrence of natural convection or buoyancy.

5 a FIGS. 5 b. The calculation of the boundary layer resistance Rbl and the fluid temperature Tm are explained on the basis of examples shown inand

5 5 a b FIGS.and 13 14 15 11 In, to estimate the fluid temperature Tm, the surface temperature Ts is measured by the first and/or second temperature sensor,and needs to be related to the fluid temperature Tm via the resistance network. The boundary layerprovides the thermal boundary resistance Rbl to transfer heat from the fluidto the wall. The thermal boundary resistance Rbl needs to be accurately calculated to ensure accuracy of non-invasive temperature measurement.

13 1 At first, physical properties of the fluid are obtained. Such properties are for example fluid velocity data and pipe and/or insulation geometry data, in particular pipe diameter D. Additionally the surface temperature Ts and the external temperature Ta are measured. The surface temperature Ts can be measured for example by the first temperature sensorand corresponds to the first temperature data T.

12 With data based on the geometry of the pipe, the pipe thermal resistance Rp is calculated and, if necessary, insulation resistance Rins too.

13 14 18 12 12 18 Rbl=f Re,Pr,x/D Tm−Ta Ts−Ta Rbl+Rp+Rins+Ra Rins+Ra 5 a FIG. In the next step, the Reynolds number Re and the Prandtl number Pr are calculated with the obtained data and the distance x from a nearest upstream feature to the first and/or second temperature sensor,is measured. With this data, a boundary layer resistance Rbl can be calculated.()  Eq. 1The boundary layer resistance Rbl allows to calculate the temperature of the fluid Tm (see).()/()=()/()  Eq. 2The external resistance Ra, varies often between 2 and 6 W/m2·K (for typical insulationsor uninsulated pipes). Therefore, the external resistance Ra does not impact the temperature measurement significantly, for insulated pipes. The insulation resistance Rins is calculated by using the insulation dimensions and thermal conductivity of the insulation.

11 Calculation of the boundary layer resistance Rbl involves calculation of the Reynolds number Re which requires fluid velocity data, density data, viscosity data and pipe diameter data. Fluid velocity data is preferably obtained by measuring. Density and viscosity data are either measured or obtained from knowledge of the fluid. The Reynolds number Re is given as:(density*velocity*pipe diameter)/dynamic viscosity  Eq. 3

5 b FIG. The Calculation of the boundary layer resistance Rbl also requires the Prandtl number Pr. Calculation of the Prandtl number Pr requires the physical properties of the fluid, the thermal conductivity, the specific heat capacity and the viscosity data, often influenced as such by local temperature. The Prandtl number Pr is given by:(dynamic viscosity*specific heat capacity)/thermal conductivity  Eq. 4The boundary layer resistance Rbl also possibly includes the Grashof number Gr or any number which accounts for natural convection or buoyancy effects leading to flow/thermal stratification across the transverse pipe cross section (see).

Rbl=f Re,Pr,x/D,Gr The Grashof number Gr is calculated based on the fluid properties.()  Eq. 5

6 FIG. 12 12 , shows a pipewith an upstream curvature with a radius R. The pipehas the diameter D.

7 FIG. 12 12 shows a longitudinal section of the pipe. The pipecomprises a top and bottom section.

8 FIG. 7 FIG. 12 20 Rbl=f Re,Pr,x/D,Gr,D/ R shows a cross section of the pipeaccording to. The boundary layer resistance Rbl in this embodiment includes a parameter accounting for circumferential variation in fluid/thermal conditions due to natural convection or buoyancy effects. Such a parameter is provided by the process condition data P. Here, a reference pointis set, so the boundary layer resistance Rbl at any circumferential location can be expressed in terms of an angle   and incorporated into the method.(2,φ)  Eq. 6The dependency of boundary layer resistance Rbl on φ can be, for example, determined by a computational fluid dynamics calculation.

12 The presence or probability of a stratification can be output in the form of an alarm. The temperature distribution across the pipeis provided as an output using several variables for lower, middle, and top temperature. To re-iterate, the model ensures that the process condition data (Nominal flow rate, pressure, density, viscosity, pipe dimensions, wall thickness and thermal conductivity of the fluid) are either input as stationary nominal parameters or even as inputs from real sensors in the vicinity and are taken into consideration.

11 FIG. 12 13 FIGS.and 1 2 In, an alternate embodiment to determine flow regimes is shown which includes the use of two surface sensors mounted with a specified distance between them and a specified distance x from the inlet of an essentially straight pipe section. The difference between the first and second temperature data Tand Tor ΔT divided by the distance separating the measurement points is dependent on the flow data F (laminar, transitional or turbulent) and hence can be correlated to the Reynolds number Re as shown in.

The correlation can be obtained by testing or computational/analytical methods. Based on the correlation, the correct Reynolds number Re can be imposed in the boundary layer resistance Rbl.

If stratification is not expected, e.g., for high-viscous fluids or for essentially vertical pipes, one surface sensor per perimeter is sufficient. On the other hand: If laminar behavior is assumed, e.g., from an (in axial direction) significantly changing boundary layer conductivity, together with other circumstances like low viscosity and/or an essentially non-vertical pipe, a warning message can be issued that Temperature inhomogeneities are expected.

12 13 FIGS.and The method requires no online flow measurement. If a flow is measured, the fluid viscosity can be calculated from the Reynolds number obtained from the relation shown in.

12 13 FIGS.and 1 2 13 14 1 2 In, first and second temperature data or pipe surface temperatures Tand Tare measured by the first and second temperature sensors,at points separated by distance x. Corresponding to first and second temperature data T-Tor ΔT the Reynolds number Re is obtained from the relation between Re and ΔT. The boundary layer resistance Rbl is modified accordingly, and the fluid temperature Tm calculated using equation 2.

14 FIG. shows the relation between a predicted temperature difference and a flow speed of the fluid, in particular a gas. The difference decreases with a growing flow speed.

11 In an alternate embodiment, the ambient temperature can be controlled so as to ensure a significant temperature difference between the fluidand the ambient. Preferably, the measurement of the surface temperature Ts should be as accurate as possible. This is possible with reasonably insulated and carefully installed cable thermometers. Also, temperatures should not be higher than approximately 100° C.

The present disclosure has been described in conjunction with exemplary preferred embodiments. However, other variations can be understood and effected by those persons skilled in the art and practicing the claimed invention, from the studies of the drawings, this disclosure, and the claims. Notably, in particular, the any steps presented can be performed in any order, i.e., the present invention is not limited to a specific order of these steps. Moreover, it is also not required that the different steps are performed at a certain place or at one node of a distributed system, i.e., each of the steps may be performed at different nodes using different equipment/data processing units.

In the claims as well as in the description the word “comprising” does not exclude other elements or steps and the indefinite article “a” or “an” does not exclude a plurality. A single element or other unit may fulfill the functions of several entities or items recited in the claims. The mere fact that certain measures are recited in the mutual different dependent claims does not indicate that a combination of these measures cannot be used in an advantageous implementation.

1 Sfirst pipe section 2 Ssecond pipe section Tm fluid temperature data 1 Tfirst temperature data 2 Tsecond temperature data Ts surface temperature Tsp predicted surface temperature Tcon condensate temperature P process condition data Rbl thermal boundary resistance data Rp pipe resistance Rins insulation resistance Ra external resistance 10 system 11 fluid 12 pipe 13 first temperature sensor 14 second temperature sensor 15 boundary layer 16 inner surface of the pipe wall 18 insulation 19 outer surface of the pipe wall 20 reference point 21 condensate

According to a first aspect of the present disclosure, a computer implemented method for providing temperature data of a fluid flowing through a pipe is provided, comprising: obtaining first temperature data from a first temperature sensor, which is arranged at a first pipe section; obtaining second temperature data from a second temperature sensor, which is arranged at a second pipe section; wherein the first temperature sensor and the second temperature sensor are non-invasive temperature sensors; providing process condition data; determining boundary thermal resistance data of a boundary layer of the fluid next to an inner surface of the pipe wall of the pipe based on said process condition data and/or based on the first temperature data and/or the second temperature data.

Optionally, the method further includes determining the temperature data of the fluid based on at least the first and/or second temperature data and the boundary thermal resistance data of the boundary layer. The first and second temperature sensors are arranged spatially offset. That means the first and second temperature sensors are distanced from each other in a longitudinal and/or a circumferential direction. The first and second pipe sections describe the positions where the first and second temperature sensors are arranged.

Additionally, an ambient temperature may be provided or measured by a third temperature sensor. By taking the ambient or environmental temperature into consideration, a better measurement may be achieved.

The first and second temperature sensor are arranged at an outside surface of the pipe wall. The outer surface of the pipe wall may comprise an insulation material which is arranged around the pipe. Moreover, the packaged non-invasive sensors may e.g., be put in contact with the outside pipe surface. If the surface is painted the paint layer may be removed in a beneficial embodiment.

The two non-invasive sensors may be positioned circumferentially opposite to each other or alternately may be positioned at a measured angle from a reference point. A nominal process temperature may be used as an input into the comparison model to predict an expected surface temperature at the mounting points of the surface sensors. A difference from the prediction can be used to determine both the presence of stratification and the temperature distribution as described above.

The first and second temperature data may comprise data of the surface temperature of the pipe. The type of data provided depends on the used sensor type. Embodiments regarding these possible configurations are discussed below.

The boundary layer can be described as the layer of the fluid, which is next to the inner surface of the wall. The stream of the boundary layer is relatively slow compared to the mainstream fluid. This layer has its own thermal resistance and contributes to the difference in temperature between the bulk temperature of the flowing fluid and the wall temperature.

Accuracy of measurement depends especially on a correct estimation of the boundary layer resistance. The boundary layer resistance is the thermal resistance of the fluid layer next to the inner surface of the pipe wall of the pipe and is an important component in the overall thermal resistance network connecting the surface temperature and the fluid temperature. Variation in boundary layer resistance, due to flow regime changes, distance of measurement point from the pipe inlet, upstream flow distorting features and natural convection or buoyancy effects causes drifts in the measured temperature.

The method comprises a prediction and/or comparison model, wherein a surface temperature may be predicted and compared to a measured surface temperature. Alternatively, or additionally, the predicted surface temperature may be based on a nominal temperature as reference. A difference from the prediction can be used to determine both the presence of stratification and the temperature distribution.

The process condition data can comprise nominal process conditions. The process condition data comprises data necessary for calculating or estimating the thermal resistance of the boundary layer and subsequently the temperature of the fluid inside the pipe. The process condition data is also used to determine flow data. The process condition data can be input manually or provided by further sensors. It is also possible that corresponding calculations are carried out offline.

A possible embodiment comprises determining flow data of the fluid based on a comparison model using the first and second temperature data and the process condition data.

The flow data can include flow state data and/or a flow regime data and/or stratification data and/or flow allocation data. Flow state data comprises information whether a stratification is present. Flow regime data comprises information if the flow is turbulent transitional or laminar. Flow allocation data indicates if there are any build-ups or allocations inside the pipe, for example crystallization and condensation build-ups. Flow data also includes if there is any concentration of product constituents.

According to a further embodiment, the process condition data comprise distance data of the first temperature sensor and/or the second temperature sensor to a reference point, in particular to a feature of the pipe. Such a feature can be an inlet or a bending of the pipe.

According to another embodiment, the process condition data comprise flow velocity data, viscosity data, density data and pipe diameter data. With this data, the Reynolds number may be calculated. The Reynolds number helps predicting flow patterns in different fluid flow situations.

According to a further embodiment, the process condition data comprise viscosity data, thermal conductivity data and specific heat capacity data of the fluid. Based on these data the Prandtl number may be calculated. The Prandtl number is defined as the ratio of momentum diffusivity to thermal diffusivity.

The Reynolds number, the Prandtl number and the distance data of the temperature sensors are advantageous to determine or estimate a precise value of the thermal resistance of the boundary layer. In other words, the thermal resistance of the boundary layer depends at least on the Reynolds number, the Prandtl number and the distance of the temperature sensor to a reference point.

In another embodiment, the process condition data comprise curvature radius data and diameter data of the pipe. A bend with a curvature with a radius R is a flow disturbance and the curvature data is therefore advantageous for determining flow data. The curvature data and the diameter data are also further factors for determining a precise value of the resistance of the boundary layer.

According to an embodiment, the process condition data comprise pressure data and/or the pipe material data and/or wall thickness data. These data help to estimate a more precise value for the resistance of the boundary layer. These data can be measured or input manually.

According to an embodiment, a thermal resistance network is determined; wherein the thermal resistance network comprises external thermal resistance data, insulation thermal resistance data, pipe thermal resistance data and the boundary thermal resistance data. The boundary thermal resistance is preferably estimated according to one of the methods above. The remaining resistances are for example measured, known, or calculated.

In a possible embodiment, the first and the second temperature sensors are circumferentially offset by an angle with respect to a reference point, wherein a nominal temperature is used to predict the surface temperature and a difference of the predicted surface temperature, and the measured surface temperature based on the first temperature sensor and/or the second temperature sensor is used to determine stratification and/or temperature distribution.

For example, the embodiment can utilize two non-invasive sensors that are positioned circumferentially opposite to each other or alternately positioned at a measured angle from a reference point. In these cases, the nominal temperature or nominal process temperature is used as an input in the comparison model to predict the expected surface temperature at the mounting points of the surface sensors. A difference from the prediction can be used to determine both the presence of stratification and the temperature distribution as described above. In all these cases, the detection of the situation with the process model can be strengthened by inputting the distance from the inlet or the radius of curvature at a bend in the piping prior to the measurement point as described in the previous embodiments. The reason is that upstream flow disturbances can reduce stratification, so that it will depend on, and grow with, the distance from the disturbances. Measuring this growth, e.g. by once or multiply repeating the setups which are described in this embodiment, can give additional confirmation of the low-flow-stratification effect.

In an embodiment, the first and second temperature sensor are arranged on the pipe with a specified distance from each other; wherein the flow regime is determined by the difference of the first temperature data and the second temperature data divided by the distance.

In this embodiment, for example, two surface temperature sensors are mounted with a specified distance between each other and a specified distance from the inlet of an essentially straight pipe section. The difference between the first and second temperature data divided by the distance separating the measurement points is dependent on the flow regime (laminar, transitional, or turbulent) and hence can be correlated to the Reynolds number. The correlation can be obtained by testing or computational/analytical methods. If stratification is not expected, e.g., for high-viscous fluids or for essentially or sufficiently vertical pipes, one surface sensor per perimeter will be sufficient. On the other hand: If laminar behavior can be assumed, e.g., from an (in axial direction) significantly changing boundary layer conductivity, together with other circumstances like low viscosity and/or an essentially non-vertical pipe, a warning message can be issued that temperature inhomogeneities are expected.

An aspect of the invention comprises a computer program product, which, when executed on computing devices of a computing environment, is configured to carry out the steps of the method according to one of the above embodiments.

Another aspect of the invention comprises a system for providing temperature data of a fluid flowing through a pipe, the system comprising: a first temperature sensor for providing first temperature data, which is thermally coupled to a first pipe section; a second temperature sensor for providing second temperature data, which is thermally coupled to a second pipe section; wherein the first and second temperature sensors are non-invasive temperature sensors; wherein the system comprises a processing unit configured to determine the temperature data of the fluid on the basis of at least the first and/or second temperature data and the boundary thermal resistance data of the boundary layer; and to determine flow data of the fluid based a comparison model using at least the first and second temperature data and the process condition data.

All references, including publications, patent applications, and patents, cited herein are hereby incorporated by reference to the same extent as if each reference were individually and specifically indicated to be incorporated by reference and were set forth in its entirety herein.

The use of the terms “a” and “an” and “the” and “at least one” and similar referents in the context of describing the invention (especially in the context of the following claims) are to be construed to cover both the singular and the plural, unless otherwise indicated herein or clearly contradicted by context. The use of the term “at least one” followed by a list of one or more items (for example, “at least one of A and B”) is to be construed to mean one item selected from the listed items (A or B) or any combination of two or more of the listed items (A and B), unless otherwise indicated herein or clearly contradicted by context. The terms “comprising,” “having,” “including,” and “containing” are to be construed as open-ended terms (i.e., meaning “including, but not limited to,”) unless otherwise noted. Recitation of ranges of values herein are merely intended to serve as a shorthand method of referring individually to each separate value falling within the range, unless otherwise indicated herein, and each separate value is incorporated into the specification as if it were individually recited herein. All methods described herein can be performed in any suitable order unless otherwise indicated herein or otherwise clearly contradicted by context. The use of any and all examples, or exemplary language (e.g., “such as”) provided herein, is intended merely to better illuminate the invention and does not pose a limitation on the scope of the invention unless otherwise claimed. No language in the specification should be construed as indicating any non-claimed element as essential to the practice of the invention.

Preferred embodiments of this invention are described herein, including the best mode known to the inventors for carrying out the invention. Variations of those preferred embodiments may become apparent to those of ordinary skill in the art upon reading the foregoing description. The inventors expect skilled artisans to employ such variations as appropriate, and the inventors intend for the invention to be practiced otherwise than as specifically described herein. Accordingly, this invention includes all modifications and equivalents of the subject matter recited in the claims appended hereto as permitted by applicable law. Moreover, any combination of the above-described elements in all possible variations thereof is encompassed by the invention unless otherwise indicated herein or otherwise clearly contradicted by context.